Asymptotic Behavior for a Nonlinear Degenerate Diffusion Equation in Population Dynamics

Abstract

We consider a spatially aggregating population model which provides the homogenizing process due to density-dependent diffusion and the dehomogenizing one due to a certain long-range transport. The result asserts that, by a balance between two processes, an initial distribution of populations forms itself into a traveling solitary wave pattern for large time, which exhibits phenomenologically a kind of aggregation of a species.